Bayesian methods : a social and behavioral sciences approach

摘要: BACKGROUND AND INTRODUCTION Introduction Motivation and Justification Why Are We Uncertain about Probability? Bayes' Law Conditional Inference with Historical Comments The Scientific Process in Our Social Sciences Introducing Markov Chain Monte Carlo Techniques Exercises SPECIFYING BAYESIAN MODELS Purpose Likelihood Theory Estimation Basic Bayesian Framework "Learning" on Prior Distributions versus Non-Bayesian Approaches Computational Addendum: R for Analysis THE NORMAL STUDENT'S-T Be Normal? Normal Model Variance Known Mean Both Unknown Multivariate Model, S Simulated Effects of Differing Priors Some Student's t Mixture Models Examples LINEAR MODEL Regression Posterior Predictive Distribution the Data Linear Heteroscedasticity Addendum PRIOR A Discussion Plethora Conjugate Forms Uninformative Informative Hybrid Nonparametric Shrinkage ASSESSING QUALITY Sensitivity Robustness Evaluation Comparing to Simple Averaging Concluding Quality HYPOTHESIS TESTING BAYES' FACTOR Hypothesis Testing Factor as Evidence Information Criterion (BIC) Deviance (DIC) Posteriors Kullback-Leibler Distance Laplace Approximation Densities Decision Definitions Regression-Style James-Stein Empirical Bayes Related Iterative Methods Background Integration Rejection Sampling Classical Numerical Gaussian Quadrature Importance Sampling/Sampling Resampling Mode Finding EM Algorithm Survey Random Number Generation Remarks Code BASICS OF MARKOV CHAIN MONTE CARLO Who Is What He Doing Chains? General Properties Chains Gibbs Sampler Metropolis-Hastings Hit-and-Run Augmentation Graphing Routines MCMC Implementing Software Solutions It's Only a Name: BUGS Specification Differences between WinBUGS JAGS Technical Epilogue HIERARCHICAL Multilevel Standard Poisson-Gamma Hierarchical Role Hyperpriors Exchangeability Instructions Running JAGS, Trade SOME THEORY Measure Probability Preliminaries Specific Defining Reaching Convergence Rates Implementation Concerns UTILITARIAN Practical Considerations Admonitions Assessing Mixing Acceleration Producing Marginal Integral from Metropolis- Hastings Output Rao-Blackwellizing Improved Death Penalty Support Military Personnel Extensions Annealing Reversible Jump Algorithms Perfect APPENDIX A: GENERALIZED REVIEW Terms Generalized Maximum Quasi-Likelihood B: COMMON PROBABILITY DISTRIBUTIONS REFERENCES AUTHOR INDEX SUBJECT